Preparation

Bring chicken, onion, carrot, garlic, chipotles, jalapeño, and 16 cups water to a boil in a large pot; skim foam from surface. Reduce heat to medium and simmer, skimming the surface frequently, until chicken is cooked through, about 1 hour.

Transfer chicken to a plate. Strain broth into another large pot. Return chiles to broth, if a spicier broth is desired; discard remaining solids. Shred chicken meat; discard skin and bones. Transfer chicken meat to a medium bowl and set aside.

Meanwhile, set pot with strained broth over medium heat and add cilantro sprigs. Bring broth to a simmer; cook until reduced to 8 cups, about 1 hour. Discard sprigs and chiles, if using. Stir in 3 Tbsp. lime juice. Season with salt, pepper, and more lime juice, if desired. Add chicken to broth. DO AHEAD: Can be made 2 days ahead. Chill until cold, then cover and keep chilled.

Attach deep-fry thermometer to the side of a large cast-iron skillet or other heavy skillet. Pour oil into skillet to a depth of 1". Heat over medium heat until thermometer registers 350°–360°. Working in batches, fry tortilla strips, turning occasionally, until crisp and golden brown, 2–3 minutes per batch. Using a slotted spoon, transfer to paper towels to drain. Season with salt.

Cook corn over a gas flame or under a broiler, turning occasionally, until charred in spots. Let stand until cool enough to handle. Cut kernels from cobs in strips. Discard cobs. (Alternatively, cook kernels in a large skillet over high heat until charred in spots.)